Finsler Surfaces with Prescribed Curvature Conditions
نویسندگان
چکیده
A generalization of Finsler structures on surfaces is proposed and the differential invariants of such structures are developed. The information obtained is then used to construct examples of Finsler structures and generalized Finsler structures which satisfy various interesting curvature conditions. In particular, examples are constructed of non-Riemannian Finsler structures on the 2-sphere whose ‘Gaussian curvature’ is constant and of non-Riemannian complete Finsler structures on the plane whose ‘Gaussian curvature’ is a negative constant. The local and global generality of the Finsler structures satisfying geometrically natural conditions is discussed using É. Cartan’s method of exterior differential systems.
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